The only explicit references to his age are in the second and third games. He was 19 in Monkey Island 2 (Phatt City Library, trying to get a card), had a birthday during the three months he was trapped in the Carnival of the Damned, and was 20 in Curse (SCUMM Actor's Guild card, Carnival of the Damned).
As Curse starts at night and the daylight in each area loops around through a full day and back to morning at the end, it's possible that the events of that game unfolded over one day, but perhaps not. Either way, I doubt the events of that game took 9 months, so if Guybrush and Elaine were on their three month honeymoon for the duration of the time between Curse and Escape, Guybrush must have still been 20 in Escape.
Now, if Telltale is pulling an Indiana Jones and making the amount of time that passed in the real world between games the same as the amount of time that passed in-game between games (and they seem to be), that would make Guybrush 29 now.
Also, if Elaine's reference to leaving her for three years is indeed an indication to the time between the first and second games, that would make him 16 in Secret and might also explain why she was so pissed off at him in Monkey 2.